Angered by reports of a secret global U.S. digital dragnet, members of the European Parliament today came to Capitol Hill to demand answers from American lawmakers and call for new limits on surveillance operations targeting longstanding allies.

"We have to closely cooperate on the question of fighting terrorism together, but it's a question of limits," said Elmar Brok, the German chairman of the European Parliament Committee on Foreign Affairs. "The limit is how can we target only fighting terrorism and not spy on everyone in the citizenship and also the leaders of the allied forces.

"It's not acceptable, for example, for espionage on Chancellor Merkel and others for more than 10 years," he said of reports that the NSA spied on Merkel's personal phone. "Therefore we have to see that the balance, the balance between security and freedom has to be established."

Claude Moraes, a British member of the EU Parliament leading the inquiry into mass U.S. surveillance, said the latest dispute over surveillance is serious and substantive: "This is not a cosmetic situation for us," he said.

"We believe that this disconnection that's going on suggests that perhaps there isn't sufficient [U.S.] appreciation … for the lack of privacy that EU citizens feel for this activity," Moraes said.

Brok and Moraes were part of an EU delegation that met for more than an hour behind closed doors with Rep. Mike Rogers, R-Mich., chairman of the House Intelligence Committee. Rogers, who has been largely supportive of the alleged NSA spying programs, emerged from the meeting to announce that he would lead a U.S. delegation to Brussels to continue the "dialogue."

"We're working from two different angles: one is to rewrite the perceptions that may be wrong in this particular - in some of these cases - and what the legitimate concerns are from the EU parliamentarians about the relationship, information collection and how it all works," Rogers said. "It's important to understand, we're going to have to have a policy conversation that is bigger than any individual intelligence agency of Europe or the U.S. I think we all agree on that, and that's why we're going to continue to have these cross-Atlantic dialogues to re-establish trust."

Rogers would not confirm or deny reports of U.S. spying on German Chancellor Angela Merkel but suggested that what some news media have reported as "absolute may not necessarily be absolute."

"It's true that we've now had allegations being made about certain leaders in some of our European countries having the same kind of experience," being subject to American surveillance, Timothy Kirkhope, a conservative British parliamentarian told ABC News. "But I haven't seen any proof and not likely to either."

"Obviously we're looking at electoral cycles that are going on around the year, there are bound to be some politics in this, and there are some in-built prejudices against the U.S. in some political parties in some countries," Kirkhope said, qualifying some of the outrage emanating from European governments over allegations of U.S. spying.

Brok said his delegation would also be holding meetings with State Department officials and other members of the Obama administration during their visit to the U.S.

"I think confidence is damaged," Brok said. We "have to work hard that confidence is reestablished between the leaders, between our people and therefore we have to find a new way that we concentrate on fighting terrorism and not spy on everyone."